David Sparks

Three‐dimensional mantle convection beneath a segmented spreading center: Implications for along‐axis variations in crustal thickness and gravity

Segmentation and along-axis variations within individual segments indicate the inherently three-dimensional nature of mantle up welling and melting beneath oceanic spreading centers. Numerical convection experiments are used to explore the effects of local buoyancy forces on upwelling and melt production beneath a segmented spreading center. The experiments are conducted in a region consisting of a thermally defined rigid lithosphere and a uniform viscosity asthenosphere overlying a higher-viscosity mantle half-space. A periodic plate boundary geometry is imposed consisting of spreading segments and transform offsets. Buoyancy forces are caused by thermal expansion and the compositional density reduction due to the extraction of partial melt. The relative magnitudes of the buoyant and plate-driven components of mantle flow are controlled by the spreading rate and mantle viscosity, with buoyant flow more important at lower spreading rates and viscosities. Buoyant flow beneath the spreading axis amplifies along-axis variations in upwelling near a ridge-transform intersection, and distributes the variations along the entire spreading axis. Buoyant flow may thus be responsible for the more three-dimensional character of slow spreading centers. Away from the spreading axis, thermal buoyancy drives convective rolls that align with the direction of plate motion and which have an along-axis wavelength controlled by the prescribed thickness of the asthenosphere. However, the position and stability of rolls are influenced by the segmentation geometry. In cases where the spreading center geometry does not allow a stable configuration of rolls, the flow is time-dependent. Along-axis variations in upwelling cause variations in melt production, which imply large variations in crustal thickness that dominate the surface gravity signal. The crustal thickness distributions implied by these numerical experiments produce bulls-eye-shaped negative mantle Bouguer anomalies centered over spreading segments, as observed at several spreading centers. The amplitude of the anomaly increases with decreasing spreading rate.

A model for porosity evolution during creep compaction of sandstones

Abstract A coupled creep-compaction and chemical-reaction model is developed to predict the porosity evolution for quartzose sandstones as a function of strain. The model also demonstrates the relative importance of grain-contact dissolution and cementation for both uniaxial and isotropic compaction. Theoretical analysis indicates that porosity reduction during compaction of sandstones is nonlinearly related to strain. In open systems, porosity loss is also related to grain packing, stress state, and pore-fluid saturation state. Grain-contact dissolution is the dominant mechanism for porosity loss in a closed system and, with increasing compaction, cementation becomes increasingly important. Compared to uniaxial compaction, isotropic compaction leads to more porosity loss due to grain-contact dissolution, but less porosity loss due to cementation. With compaction, pore-fluid saturation state has an increasing effect on porosity loss. Higher saturation state enhances porosity loss due to cementation.

A General Criterion for Liquefaction in Granular Layers with Heterogeneous Pore Pressure

Fluid-saturated granular and porous layers can undergo liquefaction and lose their shear resistance when subjected to shear forcing. In geosystems, such a process can lead to severe natural hazards of soil liquefaction, accelerating slope failure, and large earthquakes. Terzaghis principle of effective stress predicts that liquefaction occurs when the pore pressure within the layer becomes equal to the applied normal stress on the layer. However, under dynamic loading and when the internal permeability is relatively small the pore pressure is spatially heterogeneous and it is not clear what measurement of pore pressure should be used in Terzaghis principle. Here, we show theoretically and demonstrate using numerical simulations a general criterion for liquefaction that applies also for the cases in which the pore pressure is spatially heterogeneous. The general criterion demands that the average pore pressure along a continuous surface within the fluid-saturated granular or porous layer is equal to the applied normal stress.